Proclaiming Dictators and Juntas or Testing Boolean Formulae

We consider the problem of determining whether a given function ¢ £ ¤¥ ¦ §¨©  ¤¥ ¦ §¨ belongs to a certain class of Boolean functions  or whether it is far from the class. More precisely, given query access to the function ¢ and given a distance parameter , we would like to decide whether ¢   or whether it differs from every    on more than an -fraction of the domain elements. The classes of functions we consider are singleton (“dictatorship”) functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of  (the number of function variables), and polynomial in the other relevant parameters.

• Type: Conference
• Year: 2001
• Where: RANDOM
• Authors: Michal Parnas, Dana Ron, Alex Samorodnitsky
• Keywords: Boolean Functions, Certain Class, Monotone Dnf Functions, RANDOM 2001, Theoretical Computer Science